Question

find the median of the following distribution: marks: 35,45,50, 64,70,72
no. of students: 3,5,8,10,5,5.
​

Answer 1

Answer:

Step-by-step explanation:

We write the distribution in the cumulative frequency table.

Marks

        No. of students (f)

      Cumulative frequency

35  

               3

             3

45

               5

             8

50

               8

             16

64

              10

             26

70

                5

              31

72

                5

             36

Here total number of observations, n=36 which is even.

Median=  

2

1

​  

(n/2  

th

term+((n/2)+1)  

th

term)

=  

2

1

​  

(36/2  

th

term+((36/2)+1)  

th

term)

=  

2

1

​  

(18  

th

term+(18+1)  

th

term)

=  

2

1

​  

(18  

th

term+19  

th

term)

=  

2

1

​  

(64+64) [Since 17  

th

 to 26  

th

 observation is 64]

=  

2

1

​  

×128

=64

Hence the median is 64.